1

Fission Barriers of Compound Heavy NucleiPairing Reentrance Phenomenon in Heated Rotating Nuclei

Witold Nazarewicz

University of Tennessee/ORNLGanil, May 2009

Universal Nuclear Energy Density Functional

http://unedf.org/•Funded (on a competitive basis) by

•Office of Science•ASCR•NNSA

•15 institutions• ~50 researchers

•physics•computer science•applied mathematics

• foreign collaborators•FIDIPRO•Warsaw•France/Belgium•Japan

• 5 years

…unprecedentedtheoretical effort ![See http://www.scidacreview.org/0704/html/unedf.html

by Bertsch, Dean, and Nazarewicz]

3

Example:Example: Large Scale Mass Table Calculations Large Scale Mass Table CalculationsScience scales with processors

The SkM* mass table contains 2525 even-even nucleiThe SkM* mass table contains 2525 even-even nuclei A single processor calculates each nucleus 3 times (prolate, oblate, spherical) A single processor calculates each nucleus 3 times (prolate, oblate, spherical)

and records all nuclear characteristics and candidates for blocked calculations and records all nuclear characteristics and candidates for blocked calculations in the neighborsin the neighbors

Using 2,525 processors - about 4 CPU hours (1 CPU hour/configuration)Using 2,525 processors - about 4 CPU hours (1 CPU hour/configuration)

9,210 nuclei9,210 nuclei 599,265 configurations599,265 configurations Using 3,000 processors - about 25 CPU hoursUsing 3,000 processors - about 25 CPU hours

Even-Even NucleiEven-Even Nuclei

All NucleiAll Nuclei

M. Stoitsov

HFB+LN mass table, HFBTHO

Jaguar Cray XT4 at ORNL

INCITE awardDean et al. 17.5M hours

INCITE awardDean et al. 17.5M hours

see MassExplorer.org

A. Staszczak, A.Baran,J. Dobaczewski, W.N.

Multimodal fission in nuclear DFT

NNSA Grant DE-FG03-03NA00083

http://www.phys.utk.edu/witek/fission/fission.html

244Pu243Am

+ 48Ca

248Cm

ENAM’04

245Cm249Cf

237Np

226Ra238U

242Pu

ENAM’08

Cold fusion cross sections and fusion probability

10-30

10-32

10-34

10-36

10-38

102 104 106 108 110 112 114 116 118

A tom ic num ber

Cro

ss s

ectio

ns

(cm

)2

208 209 48P b, B i + C a

Z n70 N i

64 F e

58 C r

54

T i

5010-30

10-32

10-34

10-36

10-38

102 104 106 108 110 112 114 116 118

A tom ic num ber

Cro

ss s

ectio

ns

(cm

)2

K . M orita et al., J. Phys. Soc. Jpn, (2004) 2593.

S. Hofm annRep. Prog. Phys., 61 (1998) 639

208 209 48P b, B i + C a

Z n70 N i

64 F e

58 C r

54

T i

50

150 200

100

10-2

10-4

10-6

10-8

C ou lom b repu ls ion

Fu

sion

pro

bab

ility

1 5010050

Z .Z / A +A1 21/3 1 /3

200 250 300

208 16P Ob +

48Ca

Zn70

Ni

64

Fe

58

Cr

54

Ti

50

1 event / year

SHE

Ex=12-15 MeVCold fusion Act.+48Ca

Z=112-118Z=112-118

Ex=40-45 MeVHot fusion

Oganessian, ENAM’08

7

Experiments

E*=10~12 MeV

E*=35~40 MeV

E*~80 MeV

Survival probability of CN is one of the Key issues!

Fission barriers of compound superheavy nuclei

Pei, Sheikh, WN, Kerman, Phys. Rev. Lett 102, 192501 (2009)

Unique HFB solvers made this work possible:

HFBAX: J.C. Pei et al., Phys. Rev. C 78, 064306 (2008)HFODD: J. Dobaczewski and P. Olbratowski, Comput. Phys. Commun. 158, 158 (2004); ibid.167, 214 (2005)

Fission: isothermal or isentropic, or …?

M. Diebel, K. Albrecht, and R.W. Hasse, Nucl. Phys. A 355, 66 (1981)M.E. Faber, M. Ploszajczak, and K. Junker, Acta Phys. Pol. B 15, 94 (1984)

Numerical test Numerical test

The lowest minimum warmer than the saddle point!

Shell effects crucial!

Particle gas componentCan be removedIts magnitude is related to particle widthP. Bonche, S. Levit, and D. Vautherin, Nucl. Phys. A 427, 278 (1984); 436, 265 (1985)

Systematic Study of Fission Barriers of Excited Superheavy NucleiSheikh, WN, Pei, arXiv:0904.3910

Focus on:

•Mirror asymmetry and triaxiality at high temperatures•Systematic analysis of barrier damping

Transition to symmetric splitat high-T

The damping factor can bemeaningfully extracted

Meissner effect and reentrance phenomenon in heated rotating nuclei

D.J. Dean, K. Langanke, H.A. Nam, and WNsubmitted, arXiv:0901.0560

When a metal is cooled below its superconducting transition temperature Tc inthe presence of an external magnetic field, the magnetic flux inside vanishes. For type I superconductors, magnetic flux is expelled below a critical field Hc, while at H=Hc, a sharp transition to a normal conductor takes place. In type II superconductors, this transition is gradual, and it is characterized by two critical temperatures, Tc1 and Tc2. For Tc1 < T < Tc2 the system exists in thevortex (mixed) state in which the normal and superconducting phases coexist.

Type-IRecently, there has been increased interest in properties of polarized (asymmetric) Fermi systems with unusual pairing configurations. This includes the existence of superconductivity in a ferromagnetically ordered phase and an interplay between pairing, spin polarization, and temperature in condensates having an unequal number of spin-up and spin-down fermions.

What about nuclei?

H

Polarization -> Angular momentumVortices -> Broken pairs

•Mottelson-Valatin effect (1960)•Backbending and pair decoupling (1972)•Nuclei are Type-II superconductors (Birbrair 1971)

M J

The majority of investigations have been restricted to rotating cold nuclei or to non-rotating heated nuclei, thus exploring only limits of the (, T) phase diagram.

Previous work:Thermal properties of N=40 isotopes K. Langanke, D.J. Dean, WN

Nucl. Phys. A 757 (2005) 360

Temperature-induced superconductor-to-normal and deformed-to-spherical phase transition in N=40 medium-mass isotones:

• 68Ni - spherical, weakly-paired• 70Zn - spherical, superfluid• 72Ge - deformed, superfluid• 80Zr - deformed, weakly-paired

The deformed-to-spherical transition is fairly gradual, and it does not produce a peak in the specific heat.

The calculations nicely differentiate between two limits of pairing correlations. For superfluid systems (static pairing), the superfluid-to-normal transition manifests itself as a pronounced peak in the specific heat around T=0.6-0.7 MeV. For nuclei with weak (dynamic) pairing, CV increases in a smooth way. Here, the notion of a phase transition cannot be applied.

The Model

Complete fp-gds shell-model space (the Shottky peak moved to T>2 MeV)Shell Model Monte Carlo Method (SMMC)

Single-Particle Hamiltonian (56Ni) + pairing+quadrupole term

4096 statistical samples

Nuclear observables describedas thermal averages

72Ge: 12 valence protons, 40 valence neutrons

Includes time-odd physics

Highly-asymmetric pattern:interplay between alignment and pairing

One broken g9/2

neutron pair

Reentrant superconductivity

Allub, Wiecko, AlascioPhys. Rev. B 23, 1122 (1981)Ce impurities in superconductors

•S. Robaszkiewicz, R. Micnas, and J. Ranninger, Phys. Rev. B 36, 180 (1987).

•N.A. Fortune et al., Phys. Rev. Lett. 64, 2054 (1990).

•H.T. Diep, M. Debauche, and H. Giacomini, Phys. Rev. B 43, 8759 (1991).

•F.M. Araujo-Moreira, W. Maluf, and S. Sergeenkov, Eur. Phys. J. B 44, 33 (2005).

The reentrance (or partial order) phenomenon manifests itself in successive phase transitions

• BCS: R. Balian, H. Flocard, and M. Veneroni, Phys. Rep. 317, 251 (1999)

• Seniority Hamiltonian: S. Frauendorf et al., Phys. Rev. B 68, 024518 (2003); J.A. Sheikh, R. Palit, and S. Frauendorf, Phys. Rev. C 72, 041301 (2005)

With increasing temperature, less-aligned excited configurations with lower seniorities enter the canonical ensemble, and this reintroduces the pair correlations. At still higher temperatures, the Meissner transition takes place and pairing correlations decrease.

Abnormalbehavior ofspecific heat

Also:•level density•pair transfer

Two aspects of nuclear behavior at T>0

•Isentropic fission barriers and shell structure

•Reentrant superconductivity at high spins

Impact of shell effects on survival probability of superheavy compound nuclei

The role of finite-size effects on pairing in spin-polarized nuclei

SUMMARY

Thank You

Thank You